The plasma membrane defines the shape of the cell and plays an indispensable role in bridging intra-and extracellular environments. Mechanochemical interactions between plasma membrane and cytoskeleton are vital for cell biomechanics and mechanosensing. A computational model that comprehensively captures the complex, cell-scale cytoskeleton-membrane dynamics is still lacking. In this work, we introduce a triangulated membrane model that accounts for the membrane's elastic properties, as well as for membrane−filament steric interactions. The corresponding force-field was incorporated into the active biological matter simulation platform, MEDYAN ("mechanochemical dynamics of active networks"). Simulations using the new model shed light on how actin filament bundling affects generation of tubular membrane protrusions. In particular, we used membrane-MEDYAN simulations to investigate protrusion initiation and dynamics while varying geometries of filament bundles, membrane rigidities and local G-Actin concentrations. We found that the bundles' protrusion propensities sensitively depend on the synergy between bundle thickness and inclination angle at which the bundle approaches the membrane. The new model paves the way for simulations of biological systems involving intricate membrane−cytoskeleton interactions, such as those occurring at the leading edge and the cortex, eventually helping to uncover the fundamental principles underlying the active matter organization in the vicinity of the membrane.

Mechanochemical simulations of actomyosin networks are traditionally based on one-dimensional models of actin filaments having zero width. Here, and in the follow up paper (arXiv, DOI 10.48550/arXiv.2203.01284), approaches are presented for more efficient modeling that incorporates stretching, shearing, and twisting of actin filaments. Our modeling of a semiflexible filament with a small but finite width is based on the Cosserat theory of elastic rods, which allows for six degrees of freedom at every point on the filament’s backbone. In the variational models presented in this paper, a small and discrete set of parameters is used to describe a smooth filament shape having all degrees of freedom allowed in the Cosserat theory. Two main approaches are introduced: one where polynomial spline functions describe the filament’s configuration, and one in which geodesic curves in the space of the configurational degrees of freedom are used. We find that in the latter representation the strain energy function can be calculated without resorting to a small-angle expansion, so it can describe arbitrarily large filament deformations without systematic error. These approaches are validated by a dynamical model of a Cosserat filament, which can be further extended by using multiresolution methods to allow more detailed monomer-based resolution in certain parts of the actin filament, as introduced in the follow up paper. The presented framework is illustrated by showing how torsional compliance in a finite-width filament can induce broken chiral symmetry in the structure of a cross-linked bundle.

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In most eukaryotic cells, actin filaments assemble into a shell-like actin cortex under the plasma membrane, controlling cellular morphology, mechanics, and signaling. The actin cortex is highly polymorphic, adopting diverse forms such as the ring-like structures found in podosomes, axonal rings, and immune synapses. The biophysical principles that underlie the formation of actin rings and cortices remain unknown. Using a molecular simulation platform, called MEDYAN, we discovered that varying the filament treadmilling rate and myosin concentration induces a finite size phase transition in actomyosin network structures. We found that actomyosin networks condense into clusters at low treadmilling rates or high myosin concentration but form ring-like or cortex-like structures at high treadmilling rates and low myosin concentration. This mechanism is supported by our corroborating experiments on live T cells, which exhibit ring-like actin networks upon activation by stimulatory antibody. Upon disruption of filament treadmilling or enhancement of myosin activity, the pre-existing actin rings are disrupted into actin clusters or collapse towards the network center respectively. Our analyses suggest that the ring-like actin structure is a preferred state of low mechanical energy, which is, importantly, only reachable at sufficiently high treadmilling rates.

We present a multi-resolution methodology for modelling F-actin filaments. It provides detailed microscopic information at the level of individual monomers at a lower computational cost by replacing the monomer-based model in parts of the simulated filament by a rod-based macroscopic model. In the monomer-based description, G-actin is represented by ellipsoids bound at the surface in a double helical configuration to form F-actin. The rod-based model is coarser, in which Factin is described using a Cosserat model, as seen in the preceding paper. 1 The multi-resolution methodology is illustrated using three case studies, designed to test the properties of F-actin under stretching, bending, shearing and twisting. The methodology is especially suited for situations where filaments are subject to bending deformations. We investigate the limitations of using the standard Cosserat model to capture the complete torsional behaviour of F-actin, presenting its extensions which account for curvature dependent rigidities and a twist-stretch coupling to improve accuracy of the overall multi-resolution scheme.